A my at the top-level scope of a module will keep that variable contained to the module, preventing weird inter-module dependencies such as those the OP encountered with his wanton use of do.

If you put a my there, yes. But not if you put an our there. And that's fine with strict. Or if you use $::var, no my or our needed, strict still happy.

And in general, I rather see do not being used in favour of use/require and a separate namespace, than the code using do modified to satisfy strict.